New class of generating functions associated with generalized hypergeometric polynomials

In this paper authors prove a general theorem on generating relations for a certain sequence of functions. Many formulas involving the families of generating functions for generalized hypergeometric polynomials are shown here to be special cases of a general class of generating functions involving generalized hypergeometric polynomials and multiple hypergeometric series of several variables. It is then shown how the main result can be applied to derive a large number of generating functions involving hypergeometric functions of Kampé de Fériet, Srivastava, Srivastava-Daoust, Chaundy, Fasenmyer, Cohen, Pasternack, Khandekar, Rainville and other multiple Gaussian hypergeometric polynomials scattered in the literature of special functions.     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

On Zagier’s cusp form and the Ramanujan τ function

Zagier constructed a cusp form for each weightk of the full modular group. We use this construction to estimate Fourier coefficients of cusp forms. In particular, we get a non-trivial estimate, by elementary methods and indicate a relationship with the Lindelof hypothesis for classical Dirichlet L-functions. Dedicated to the memory of Professor K G Ramanathan     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

Standard pseudo-Hermitian structure on manifolds and seifert fibration

A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function onM. AsM supports a contact form, there exists a characteristic vector field dual to the contact structure. If induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature or of nonpositive curvature . By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday     

可能性理论的推广方法及合理性研究

本文通过引入二维可能性分布函数的概念，将可能性测度推广到二维的情形。并给出了二维可能性测度的一些重要性质。文中还重点证明了该推广方法的合理性。     

Hopfield型模型的收敛性

本文考虑Ｈｏｐｆｉｅｌｄ型模型的收敛性问题和吸引子的吸引域的刻画。证明了Ｎ＜＋∞与Ｎ＝＋∞时Ｈｏｐｆｉｅｌｄ模型在几乎处处的意义下收敛于吸引集。当Ｎ＜＋∞时，模型将在有限时间内稳定于某一吸引子上．对于Ｎ＜＋∞与Ｎ＝＋ ∞的情形，分别得到了吸引域的一个集的刻画。     

Equilibrium theory for the hard-core systems

It is found that the density expansion in the argument of the exponential function gives a fine convergence on the equation of state of the hard-sphere system. The pair distribution function and the equation of state is constructed by an intuitive kinetic theoretical method. The equation of state of the hard-core system with attractive potential is constructed semiempirically with the aid of this simple analytical result, and Kamerling-Onnes' constant of the critical point is obtained analytically.